Since gravity has the ability to escape from a black hole, our model must be incomplete. Relative to a moving mass nearby a rotating black hole, as the rotation rate gets higher and higher (relative to c), a portion of the black hole (a conical region), should disappear (its relative speed appearing higher than c). Similarly, it has been observed that the gravitational field "bulges" along the plane perpendicular to its axis of rotation. The effective gravity should be taking the relative speeds of the masses into account. The equation for gravitational attraction would probably be :

with the caveat that the relative velocity can never be bigger than -c and has implied limits of 2 and 0. The gravitational event horizon is thus for mass which has been moving ever since the Big Bang into our forever non-visible universe and for mass that accumulates onto black holes that spin at nearly c.

Another "constant" that is very difficult to measure with precision is the sun's energy output. Meteorological (weather) services the world round use pyroheliometers, which use a black surface to absorb the sun's energy with a thermopile sensor's output measuring the differential temperature between the black surface and ambient temperature. The sensor itself is housed in a hemispherical Dewar (vacuum bottle). As you can guess, there is no end to the uncertanties of this sensor, from the optics of the Dewar and thermal leakage to the changing absorption properties of the "black" body as it is exposed to radiation.

Meteorologists from the world gather each year at the time of the summer solstice on a mountain top, pick a clear day and after a countdown take readings from their "reference" instruments. These instruments are then used as transfer standards based on the assumption that the sun's output is constant.

While there is a lot of data showing the sun's output variations in the short term, there is no sensor stable enough to read the sun's long term variability.

As we all know, the sun provides the energy feeding our weather. But the sun's varying output is not a variable in any climate models. Being unmeasurable, it is assumed to be constant. Most scientists attribute past climate changes, from ice ages to tropical conditions in the Antarctic to varying solar output.

"Yet, as most engineers and scientists know, getting consistent, accurate results in any test-and-measurement challenge to better than three or four significant figures is rarely easy. Every added significant figure means ever-more-subtle sources of error must be uncovered, understood, calibrated out, or compensated for in the fixture and equipment."

How many significant figures are currently possible in state-of-the-art scientific research?

Annual global mean sea level rise is currently estimated to be 2.28 mm/yr. The newest and most precise satellites having this ability, Jason-1 and Jason-2, orbit at a mean altitude of 1336 km (1.336 billion mm). Detecting a 1 mm change in sea level would require a measurement uncertainty of less than one part per billion.

Many factors can affect a satellite's position: Mountain ranges have more mass, and therefore more gravity, than prairies. The moon and sun have strong gravitational attraction. The solar wind is variable and turbulent. When the satellites' orbits begin to decay, booster rockets are fired to restore their altitude. All of this has to be modelled and corrected for.

A RADAR altimeter is used to measure sea surface height relative to the satellite. Two RADAR frequencies are used so that the effects of atmospheric moiisture can be accounted for. Higher ocean waves result in earlier arrival of initial RADAR reflections. A correction can be made by looking at all reflected energy, not just the earliest, but this correction depends on assumptions about the shape of sea surface waves.

The satellites complete one orbital cycle every 10 days, and they are separated by 5 days, so the sea surface height is measured only once every 5 days at each location. According to the Nyquist sampling theorem, that means any sea surface waves having a period less than 10 days will undergo temporal aliasing because the sampling rate is too low to capture the true waveform.

NASA goes to great lengths to make the satellite altimetry measurements as precise as possible. For example, the GRACE satellite mission maps the earth's gravity field, and this data can then be used to improve the real-world models used by the Jason missions.

My question is: Can I really believe the claims of one part per billion accuracy in the global mean sea level data? My gut is saying 'no', but I was wondering if someone with experience in this area could shed any light.

I think you can believe them for this simple reason: the chances that complete amateurs can find holes in the work of professionals is extremely low. You put together a good argument, but I think the chances of you having thought of something they haven't is very low indeed. You must have a speciality, a day job. What do you think the chances are that they'd spot something you hadn't thought of in one of your projects?

@jackxxxx: My guess is that you (presumably as an engineer) never read the classisc Hans Christian Andersen story "The Emperor's New Clothes." Otherwise you might be a bit skeptical about "expert" opinion. Anytime I hear the phrase " but everybody knows..." in an informal debate I know then and there that the speaker is WRONG! Consensus is not truth. If it were, the sun would be in orbit arounbd the earth.

Well, in a way it is ... they are both orbiting each other, but the sun is so much more massive that the effect of the Earth on it is miniscule. This effect is much more pronounced with regard to the Earth and Moon, which orbit about their barycentre (common centre of mass) that lies about 4600 km from the Earth's centre (about three quarters of the Earth's radius).